Disha Expert Team Solutions for Chapter: Fundamental Operations, Vbodmas Rule, Approximation and Simplification, Exercise 1: Exercise

If '$a$' be a positive number then the least value of $a+\frac{1}{a}$ is _____.

The value of $\frac{0.051\times 0.051\times 0.051+0.041\times 0.041\times 0.041}{0.051\times 0.051\times 0.051-0.041\times 0.041\times 0.041}$ is?

Calculate the number of digits in the product of $4^{11111}\times 5^{22222}=$?

If $\left(x+y+z\right)=6$ and $\left(xy+yz+zx=11\right)$, then the value of $\left(x^3+y^3+z^3-3xyz\right)$ is _____.

If $\left(x+\frac{1}{x}\right)=2\sqrt{3}$, then the value of $\left(x^3+\frac{1}{x^3}\right)$ is:

If $x=997, y=998, z=999$, then the value of $x^2+y^2+z^2-xy-yz-zx$ will be _____.

If $x^2+y^2+2x+1=0$, then the value of $x^{31}+y^{35}$ is?

$\frac{{\displaystyle \frac{1}{3}.\frac{{\displaystyle 1}}{{\displaystyle 3}}.\frac{{\displaystyle 1}}{{\displaystyle 3}}+\frac{{\displaystyle 1}}{{\displaystyle 4}}.\frac{{\displaystyle 1}}{{\displaystyle 4}}.\frac{{\displaystyle 1}}{{\displaystyle 4}}-3.\frac{{\displaystyle 1}}{{\displaystyle 3}}.\frac{{\displaystyle 1}}{{\displaystyle 4}}.\frac{{\displaystyle 1}}{{\displaystyle 5}}+\frac{{\displaystyle 1}}{{\displaystyle 5}}.\frac{{\displaystyle 1}}{{\displaystyle 5}}.\frac{{\displaystyle 1}}{{\displaystyle 5}}}}{{\displaystyle \frac{1}{3}.\frac{{\displaystyle 1}}{{\displaystyle 3}}+\frac{{\displaystyle 1}}{{\displaystyle 4}}.\frac{{\displaystyle 1}}{{\displaystyle 4}}+\frac{{\displaystyle 1}}{{\displaystyle 5}}.\frac{{\displaystyle 1}}{{\displaystyle 5}}-\left(\frac{{\displaystyle 1}}{{\displaystyle 3}}.\frac{{\displaystyle 1}}{{\displaystyle 4}}+\frac{{\displaystyle 1}}{{\displaystyle 4}}.\frac{{\displaystyle 1}}{{\displaystyle 5}}+\frac{{\displaystyle 1}}{{\displaystyle 5}}.\frac{{\displaystyle 1}}{{\displaystyle 3}}\right)}}$ is equal to _____.